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The purpose of this article is to conduct a mathematical and phenomenological comparison of three concepts: (1) the finite limit of a function at a point, (2) the finite limit of a sequence, and (3) the infinite limit of a sequence. Additionally, we aim to analyse the presence of these concepts in Spanish textbooks. The methodology employed is exploratory and descriptive. Our mathematical comparison revealed differences in several areas, including the dependence between variables, the involved infinite processes, the types of infinity, the dimensioning for each variable, and the intuition of continuity in the interval. Our phenomenological comparison found a correspondence between phenomena using a formal approach, but differences in phenomena when using an intuitive approach. Finally, our analysis of textbooks revealed that all three limits are most commonly presented in the verbal representation system and definition format.

This article presents a reflection on a teaching experience involving the use of the Brügner tangram, an interesting but little-known manipulative material. It details an activity conducted as part of an undergraduate mathematics education course for prospective primary school teachers. The main objective of this paper is to present the implementation of a sequence of activities designed to convey to future teachers the importance of systematically solving problems that involve searching for or constructing different cases. Specifically, participants are provided with the three pieces of the Brügner's tangram and assigned the task of identifying all possible convex polygons that can be constructed. Moreover, they are required to elucidate the methodological approach underpinning their exploratory process, with an emphasis on establishing relationships between the polygons. Graphs are introduced as one of the possible approaches for modelling the problem, offering a graphical representation that aids in the systematic search for solutions. This paper describes different activities involving the Brügner's tangram which has demonstrated its adaptability as an instructional resource. The teaching sequence adheres to the five-phase structure proposed within the framework of the van Hiele model, which is also part of the course.

The Van Hiele model of geometric reasoning establishes five levels of development, from level 1 (visual) to level 5 (rigor). Despite the fact that this model has been deeply studied, there are few research works concerning the fifth level. However, there are some works that point out the interest of working with activities at this level to promote the acquisition of previous levels. Our goal is to describe this level through the construction and validation of a list of indicators for each of the processes involved in geometrical reasoning (definition, proof, classification, and identification). Due to the lack of previous research, we have decided to use the Delphi methodology. This approach allowed us to collect information from a panel of experts to reach a consensus through a series of phases about the indicators that describe each of the processes. The final product of the iterative application of this method is a list of validated indicators of the fifth Van Hiele level of reasoning. In particular, proof and definition processes have turned out to be the most relevant processes at this level.

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with graphs. We have thus analysed them adapting the methodology for computing the degrees of acquisition of the Van Hiele levels. Our analysis leads to different proof profiles of Graph Theory students whose characteristics provide empirical support to consider proof levels in Graph Theory from the perspective of the Van Hiele model.

This paper analyses how pre-service teachers approach the notion of the infinite limit of a sequence from two perspectives: Specialized Content Knowledge and Advanced Mathematical Thinking. The aim of this study is to identify the difficulties associated with this notion and to classify them. In order to achieve this, an exploratory qualitative approach was applied using a sample of 12 future teachers. Among the results, we can affirm that pre-service teachers mainly use algorithmic procedures to solve tasks in which this type of limit is implicit, although they would consider a resolution that specifically involves the notion with an intuitive approach if they had to explain it to their students.

In this work, we show the results of a research with pre-service mathematics secondary teachers about their Van Hiele level regarding the proof in Geometry. We observe three different profiles whose characteristics are described. These descriptions allow us to foresee certain differences when carrying out proof teaching in secondary school. The presence of a profile with a lower level than that assumed for some high school students stands out. The other two profiles show differences regarding the presence of some advanced proof strategies.

The development in mathematical flexibility should be included in the mathematics teaching training of students in Primary Education Degree. Teachers in training have to acquire the skill to modify the problem resolution and be able to break with stereotyped methods. This document presents an analysis of spontaneous mathematical flexibility developed by teachers in training against problems in which the calculation of the area is requested. At the same time what type of statement can promote is analysed, in a more effective way, a flexible thought and the comparison of the possible mathematical flexibility between the different problems is established.

Background: A positive conception of sexuality among people with intellectual disabilities is crucial and relies on several social and interpersonal contexts. The goal of this study is to analyse the interaction and impact of three different contextual groups: individuals with intellectual disabilities, their parents, and professionals working with them. Methods: Survey data were collected from 330 people with intellectual disabilities attending occupational centres in eastern Spain, 330 parents, and 100 professionals. Results: Correlation and variance analyses of dyad-level data show significant differences among the three groups in all variables. Professionals perceived people with intellectual disabilities to have higher knowledge of socio-sexual norms than people with intellectual disabilities actually appear to be, but they are also more concerned about aspects related to this area of people with intellectual disabilities. Compared to people with intellectual disabilities and professionals, parents perceived people with intellectual disabilities to have lower sexual knowledge. Conclusions: Our study demonstrates inconsistent perceived knowledge of people with intellectual disabilities' socio-sexual norms and sexual knowledge among the three groups, leading to disparate levels of concern regarding people with intellectual disabilities sexuality. Thus, the need to collect information from different perspectives for more accurate reporting and the critical need for sex education programs that involve the target population, but also parents and professionals who frequently interact with people with intellectual disabilities are highlighted.

Contribution: Prior studies on pedagogical methodologies to acquire soft skills have shown that developing collaborative tasks produces positive impact in students' abilities. In this article, a pedagogical approach based on interdisciplinary practice and realistic problems is proposed to improve students' teamwork skills. Background: Traditionally, soft skill acquisition has received scarce attention in high education curricula. Consequently, students finish their studies without having developed important competencies, such as communication, conflict resolution and teamwork skills. Intended Outcomes: Students who follow a realistic interdisciplinary approach improve both their soft and hard skills compared to students who follow a traditional collaborative pedagogical methodology. Through the approach proposed, students progress in completing tasks, participating in the team, collaborating in the organization, accepting agreements and taking into account the others' points of view. Application Design: The experience involved students from two different disciplines, prospective computer science engineers and preservice teachers. They worked together to design an educational application that required prospective engineers to apply Human-Computer Interaction fundamentals. A quasi-experimental study was performed using either knowledge tests or self-assessment pre-post-tests, both subsequently analyzed using quantitative methods. Findings: 1) The prospective CS engineers who followed the interdisciplinary realistic practice approach achieved better learning outcomes than those who did not; 2) the educational context affects teamwork skill development; and 3) students improved their ability to work and participate in the team after the experience.

In this document, we search for and define an infinite limit of sequences that is correct and accepted by the mathematical experts, the final purpose of which is to analyze its phenomenology, in Freudenthal's sense. To make the choice, experts were consulted on two issues. The first one was not decisive because of the effect that the divergence term causes, and for this reason, we did a second expert consultation where this term was removed and we selected the definition we have analyzed in this document. Once the definition was chosen, two approaches were considered for analysis: the intuitive approach and the formal approach. Based on these two approaches, we specify certain phenomena organized by the definition: unlimited intuitive growth and unlimited intuitive decrease (intuitive approach) and one way and return infinite limit of sequences (formal approach), and show examples of such phenomena by graphical, verbal and tabular representation systems. All this aim to be a help to overcome the difficulties that pre-university students have with the concept of limit.

Background: Despite the relevance of assessing sexual knowledge in people with Intellectual Disability, there is a lack of appropriate assessment tools to measure this domain. The current study tests the psychometric properties of the new 'Inventory of Sexual Knowledge of people with Intellectual Disability' (ISK-ID). Method: 345 individuals with mild intellectual disability completed the ISK-ID before and after the implementation of a sexual education program. Psychometric properties of the ISK-ID were analysed according to Multidimensional Item Response Theory (MIRT). Results: Its underlying factorial structure, along with parameters derived from the MIRT (item discrimination, difficulty, and participant's ability), support the use of the ISK-ID as a measure of sexual knowledge. Moreover, the ISK-ID was able to detect changes in the level of sexual knowledge resulting from educational interventions (i.e., responsiveness). Conclusions: The ISK-ID is an appropriate assessment tool to measure sexual knowledge in men and women with mild intellectual disability.

Background: This paper presents psychometric properties of an instrument for the Assessment of Sexual Behaviour and Knowledge of people with Intellectual Disability (ASBKID), other-reported by professionals who are in daily contact with them. Methods and procedures: Assessments of 236 individuals with intellectual disability were obtained from 100 professionals. Results: Confirmatory factor analysis revealed a four-factor structure: concern about the user's inappropriate or uninhibited sexual behaviour; perception of the user's knowledge about privacy and social norms; perception of the user's knowledge about sexuality; and concerns about the user's sexuality. A multi-group CFA was also conducted in men and women, confirming the adequacy of this four-factor structure by gender. The reliability of the factors ranged from 0.74 to 0.92. Conclusions: The psychometric results obtained support the use of the ASBKID as a valid and reliable measure for the assessment of sexual behaviour and knowledge in both men and women with intellectual disability.

Background: This paper presents a description of the development and psychometric properties of a self-report instrument for the assessment of sexual behaviour and concerns of people with mild intellectual disabilities (SEBECOMID-S). Methods and procedures: The study included 281 people with mild intellectual disabilities. The psychometric properties were examined through exploratory factorial analysis, descriptive statistics, and reliability indices. Results: The exploratory factor analyses offered a structure with three factors: concern about the appropriateness of their sexual behaviour, sexual practices performed, and safe sex practices. The model presents an excellent fit (?[superscript 2]/df = 1.10, RMSEA = 0.019, CFI = 0.997, TLI = 0.995, and SRMR = 0.065). General test reliability was good ([alpha] = 0.77, [omega] = 0.76). Conclusions: SEBECOMID-S is a valid and reliable tool to obtain objective information about the sexual behaviour and concerns of people with mild intellectual disabilities. The use of this instrument will make it possible to adjust their training to their real experiences, making it more effective.

The use of original sources is a useful resource not only to be used with secondary school students but also with prospective mathematics teachers. In this work, we designed a series of tasks based on a fragment excerpted from Clairaut's "Éléments de Géométrie" to be carried out with 24 participants enrolled on a Masters' Degree in Secondary School Mathematics Teaching. This fragment was chosen both due to its content and to its narrative structure and our main goal was to determine which elements of professional knowledge were used by prospective secondary mathematics teachers when reading this fragment. In order to do so, we used the MKT model as an analytical tool and we also assessed some aspects related to literacy skills. The prospective teachers were able to recognize mathematical and pedagogical components within the source that relate to their future practice. In addition, the participant's literacy skills seem to play a role in the richness of their reading.

Background: Studies have shown the role played by perceived self-efficacy in explaining condom negotiation and condom use. Aims: The factorial structure and the psychometric properties of the Brief Condom Use Self-Efficacy Scale are presented. Method: The study included 368 men and 456 women aged 17 to 55 years (M[subscript age] = 25.01, SD = 6.93). Results: Exploratory factor analysis yielded three factors: fear of rejection, impulse control, and condom acquisition and negotiation, which together accounted for 68% of the total variance. That structure was confirmed through confirmatory factor analysis. Cronbach's alpha for the Brief Condom Use Self-Efficacy Scale was 0.71. The scale provided adequate convergent validity, and positive correlations were observed between self-reported condom use and self-efficacy for use of other barrier methods. Discussion: This brief instrument could be a useful and appropriate measure to assess the types of condom use self-efficacy that occur at the different moments of a sexual relationship.

Massive Open Online Courses (MOOCs) and Open Educational Resources (OER) are rapidly growing, but are not usually offered in multiple languages due to the lack of cost-effective solutions to translate the different objects comprising them and particularly videos. However, current state-of-the-art automatic speech recognition (ASR) and machine translation (MT) techniques have reached a level of maturity which opens the possibility of producing multilingual video subtitles of publishable quality at low cost. This work summarizes authors' experience in exploring this possibility in two real-life case studies: a MOOC platform and a large video lecture repository. Apart from describing the systems, tools and integration components employed for such purpose, a comprehensive evaluation of the results achieved is provided in terms of quality and efficiency. More precisely, it is shown that draft multilingual subtitles produced by domain-adapted ASR/MT systems reach a level of accuracy that make them worth post-editing, instead of generating them ex novo, saving approximately 25%-75% of the time. Finally, the results reported on user multilingual data consumption reflect that multilingual subtitles have had a very positive impact in our case studies boosting student enrolment, in the case of the MOOC platform, by 70% relative.

Discrete-trials teaching (DTT) is a frequently used method for implementing Applied Behavior Analysis treatment with children with autism. Fazzio, Arnal, and Martin (2007) developed a 21-component checklist, the Discrete-Trials Teaching Evaluation Form (DTTEF), for assessing instructors conducting DTT. In Phase 1 of this research, three experts on DTT rated all 21 components of the DTTEF as very important, demonstrating its high face validity. In Phase 2, the DTTEF had high interobserver reliability for live scoring of trainees' DTT performances, and it differentiated between the DTT performances of trainees before and after receiving instruction in applying DTT. In Phase 3, the DTTEF evaluations of the DTT performances of trainees in Phase 2 compared favorably to ratings of video clips of those performances by DTT experts, demonstrating high concurrent validity. (Contains 2 tables and 1 figure.)

An essential component of applied behavior analysis programs for teaching children with autism is discrete trials teaching. Experiment 1 investigated the effectiveness of a self-instructional manual for teaching university students to correctly apply discrete-trials teaching to teach three tasks to confederates role-playing children with autism. Experiment 2 investigated a training package consisting of the self-instructional manual combined with accurate scoring of a videotape of an experienced tutor conducting discrete-trials teaching with a confederate role-playing a child with autism. The results suggest that self-instructional strategies have considerable potential for instructing participants to conduct discrete-trials teaching. (Contains 3 tables and 2 figures.)

The current study has a twofold purpose: first, to determine the reliability of a tool for assessing orthographic development in Spanish; second, to assess differences in students' performance on the measure across multiple types of primary schools in a large city in Chile. A Spanish developmental spelling inventory that contained words of increasing orthographic difficulty was administered twice to students in first through fifth grades in three types of schools: public, private and partially subsidised. These school types in large part represent varying levels of student socio-economic status because of costs associated with attending them. Results demonstrate that (a) the Spanish spelling inventory is able to reliably measure the development of orthographic knowledge in Spanish, and (b) there is a relationship between school type and student achievement. The authors describe individual cases to highlight the qualitative nature of differential performance for students in greater- or lesser-resourced schools.

Although the demand for training individuals to implement discrete-trials teaching (DTT) is high, published studies on strategies to do so are few. We used a modified multiple-baseline design across participants to evaluate a training package for teaching university students to implement a 19-component DTT procedure to teach three tasks to a confederate role-playing a child with autism. Also, in an AB within-subject design with each participant, we compared the two components of the training package, a self-instructional manual and feedback plus demonstration. After an average of 2.6 h to master the training manual, participants' DTT accuracy while teaching a confederate improved from 34% in baseline to 66%. After one to three sessions of feedback plus demonstration of teaching one task, DTT performance averaged 92% on that task. Participants' DTT performance generalized to the other two tasks (mean accuracy of 94%) and to teaching the tasks to a child with autism (mean accuracy of 91%). (Contains 1 figure and 3 tables.)

Discrete-trials teaching (DTT) is commonly used to implement applied behavior analysis treatment for children with autism. The authors investigated a revised self-instructional manual for teaching university students to implement a 21-component DTT procedure to teach three tasks to confederates role-playing children with autism. Also, as a motivational contingency, for each DTT session in which a student scored at or above 90% accuracy, they received US$10. After an average of 4.5 hr to master the training manual, students' average DTT performance improved from 52% in baseline to 88% while teaching a confederate. Students averaged 77% DTT performance during subsequent generalization sessions with a child with autism. (Contains 1 table and 1 figure.)

Early intensive behavioral intervention (EIBI) has been identified as the treatment of choice for children with autism spectrum disorders. A common strategy for conducting EIBI is discrete-trials teaching (DTT). There is a demand for research-based, economical, rapid training techniques to teach tutors and parents of children with autism to conduct DTT. This paper provides a review of research that has focused on teaching individuals how to conduct DTT. Considering the high demand for personnel trained in delivering DTT to children with autism, research in this field is highly warranted. (Contains 1 figure and 2 tables.)

One approach used to help find missing children is to place posters of them at the exits of supermarkets. The present research addresses the question of how effective that approach is likely to be. Posters of 8 missing children were displayed on a bulletin board at a cooperating grocery store. Customers leaving the store completed a survey and took a recognition memory test for the children. Most customers thought the problem of missing children was an important issue. However, the majority of customers also reported either not looking at the posters or only briefly looking at the posters. Recognition memory for children depicted in the posters did not reliably differ from chance. It appears that there is much room for improvement when it comes to increasing the attention paid to posters meant to help find missing children. (Contains 4 figures and 4 notes.)

This paper is based upon two empirical studies, which identify care-giving responsibilities as a key mediator of mature students'--a target group within the widening participation strategy--experiences of higher education. Employing a feminist lens on care, we identify a disjuncture between how students experience the challenges of negotiating care and study, and the narrow and economistic way care is addressed within higher education policy. We point to the broader recognition of care emerging within New Labour's policies on the reconciliation of paid work and family life and argue that in the context of increasing expectations that learning is for life, care needs to be recognised in a broader form at the interface of both education and employment. Drawing on the notion of a "political ethics of care", we conclude by identifying elements that should be included in a higher-education "care culture". (Contains 2 tables and 8 notes.)

Beyond the presupposed cleavage between economics and ethics, the institutional dimension of economic ethics needs to be emphasized. The firm can use a large scope of instruments in order to formalize economic ethics. The asset of ethical standards is that they represent a specific way of coordination. They engender positive effects such as the fall of coordination cost and the reduction of uncertainty. Ethical standards can be regarded as a way to obtain information. The central issue regarding ethical standards remains their origin and construction. This article analyses the role that international ethics standards play in markets. To begin with, we describe the link between economic ethics, firms and markets. This leads to the question of formalization of ethics in firms. The hypothesis is that international ethical standards have a specific status at an industrial policy level. The main issue that remains is, of course, the legitimacy of ethical standards and of the international organizations that develop these standards. Legitimacy and efficiency are both necessary for ethical standards, which brings to light the hybrid character of the standardization process. It has its specific place between the pressures of the market and the supervision of authorities. (Contains 2 notes.)

False memories are sometimes accompanied by surprisingly vivid experiential detail that makes them difficult to distinguish from actual memories. Such strikingly real false memories may be produced by a process called content borrowing in which details from presented items are errantly borrowed to corroborate the occurrence of the false memory item. In 2 experiments using think-out-loud protocols at both study and test, evidence for content borrowing occurred for more than half of the false remember judgments participants reported. The present study also provides evidence consistent with recollection rejection and distinctiveness playing a role in false-memory editing.